The only other word that rivals its universality is “taxi”. Ok is ok everywhere, its meaning clearly understood even when it is pitched differently.

So, how did it come into being?

It seems a slang fad floated through New York and Boston in 1838 – 39. Common phrases were shortened and deliberately mis-spelt for fun. K G stood for “no go” as if its spelling was “know go”. “All correct” became “oll korrect” and so “ok”. (”N.G.” for “no good” and “P.D.Q.” for “Pretty Damn Quick” are used even today and how about O W for “oll wright”?)

A slang phrase is usually confined to a group and is eventually forgotten. But ok had a lucky break. Martin van Buren, the democratic president hailing from the New York village Old Kinderhook decided to fight a re-election. His supporters formed the OK Club to canvass. Van Buren lost, the word stuck. By this time, OK’s usefulness as a short form to express approval had been recognised. The noun was born in 1841, the verb in 1888.

In 1919, Prez Woodrow Wilson spelt it as “okeh”, thinking it represented the Choctaw okeh (”it is so”). By 1929, “okay” got entrenched.

In 1932, students were chanting “okey-doke” and Greek immigrants in America who returned home in the 20s, were quickly labeled “okay boys” because of their US accent.
When US troops travelled all over the world during World War II they found the word being used commonly to the same meaning.
Oh, there are other theories too about this universal expression. Is it from the Scots och aye! (or perhaps Ulster Scots Ough aye!), “yes, indeed!”?

From West African languages like Mandingo (O ke, “certainly”) or Wolof (waw kay, “yes indeed”)?

From Finnish oikea, “correct, exact”? French au quais, “at the quay”?

From French Aux Cayes (a port in Haiti famous for its superior rum)? All false.
Whatever it is, the word has come to stay. Its meaning depends on how you say it. This versatility will keep it alive wherever it is said.